1. Field of the Invention
The present invention concerns a system for determining the bidimensional characteristic function of a continuous optical conversion member.
2. Description of the Prior Art
The continuous optical conversion member is an optical instrument or opto-electronic image-forming means such as, for example, a lens, a photographic object, a photographic film, an optical fiber or a photoconductor drum of a photocopier, facsimile machine or printer. The bidimensional characteristic function allows quantification of the deterioration of images produced by the continuous member in response to illumination thereof, and in particular a measurement of the attenuation in the contrast of these images as a function of the spatial frequency of optical waves illuminating the continuous member. In the case of lenses, photographic films and photoconductor drums, for example, the images produced are respectively optical images, photographic negatives and images printed on paper.
FIGS. 1 and 2 show a system for determining the bidimensional characteristic function of a discrete photosensitive cell. The system comprises a lamp 10, a focusing and collimating optical device 11, a pattern MIRE from FIG. 2, a drive means 12 for moving the pattern in two directions, an image analyzer 13 of which one of the photosensitive cells CP.sub.1,1 to CP.sub.N,P is to be characterized, and a calculator 14.
Referring to FIG. 2, the pattern MIRE is a rectangular plate transparent at wavelengths of a light beam, for example a glass plate, one side of which has a plane surface S2 which is opaque at 46 wavelengths, as shown by the shaded area. This. opaque surface is delimited by the edges of the plate and the sides of an angle greater than 180.degree. facing one corner of the plate. In the illustrated embodiment, the angle greater than 180.degree. is equal to 270.degree. and has an apex with coordinates (xi,yj) in a Cartesian system of axes (x,y) in the plane of the pattern. The opaque surface S2 is obtained by depositing a thin layer of aluminum, for example, in the shape of a dihedron having a "thickness" substantially equal to half of one of the dimensions, width or length, of the plate. The surface S1 complementary to the opaque surface S2 on the plate is delimited by a complementary angle less than 180.degree., equal to 90.degree. in the illustrated embodiment, and is transparent. In an alternative embodiment, the transparent and opaque nature of the surfaces S1 and S2 are interchanged, the opaque surface being then a rectangular surface portion with a right angle less than 180.degree. at the apex (xi,yj).
A light beam produced by the lamp 10 is projected through the optical device 11 to form a collimated light beam collimated on one side of the pattern. The edges of the glass plate constituting the pattern are trapped in a frame fastened to the moving member of a vertical motorized micrometer table constituting the drive means 12 so that the pattern can be moved in two directions orthogonal to the optical axis AA' of the device 11 and situated in a plane parallel to and a few centimeters away from the plane of the discrete photosensitive cells CP.sub.1,1 to CP.sub.N,P of the analyzer 13. One cell CP.sub.n,p from the cells CP.sub.1,1 to CP.sub.N,P is substantially coincident with the apex of the angle less than 180.degree. on the pattern for a given position of the pattern. The illumination passing through the pattern is null "0" via the opaque surface S2 and maximal "1" via the transparent surface S1. A first portion of the sensitive surface of the photosensitive cell CP.sub.n,p therefore receives a maximal illumination "1" and a second portion of the sensitive surface receives a null illumination "0". Accordingly, an image of the pattern is formed on the surface of the photosensitive cell. These first and second portions of the sensitive surface of the photosensitive cell CP.sub.n,p are delimited, like the first and second surfaces S1, S2 of the pattern (FIG. 2), by the sides of a right angle greater than or less than 180.degree.. For given coordinates (xi,yj) of the apex of the right angle greater than 180.degree. on the opaque surface of the pattern, the photosensitive cell CP.sub.n,p produces an electrical signal R.sub.xi,yj whose amplitude is equal to: ##EQU1## where x and y are two variables respectively defined by the width and height of the sensitive surface of the photosensitive cell, C(x,y) is the bidimensional characteristic function of the photosensitive cell, with c(.infin.)=0, and I(x,y) is the illumination function defined by: ##EQU2##
Let R.sub.u,v be the two-variable continuous function associated with the previously mentioned two-variable discrete function R.sub.xi,yj and defined for any pair (u,v) in the system of axes (x,y) in the plane of the pattern. ##EQU3## because I(x,y)="1" for x&gt;u and y&gt;v.
This last result can be written: ##EQU4##
The partial derivative with respect to v of the function defined by equation (1) is equal to: ##EQU5##
Consequently, the double partial derivative of the function R.sub.u,v with respect to u and v is equal to C(u,v).
This remarkable mathematical result is applied to the previously defined discrete function R.sub.xi,yj. in the following way.
Under the control of the calculator 14, the drive means 12 moves the pattern MIRE in the plane of the pattern, which is the plane of the Cartesian system of axes (x,y). The apex of the angle greater than 180.degree. of the opaque surface S2 of the pattern is therefore located at several successive positions with abscissae xi such that x1.ltoreq.xi.ltoreq.xI and ordinates yj such that y1.ltoreq.yj.ltoreq.yJ, coinciding with respective discrete points of an area including the sensitive surface of the photosensitive cell CP.sub.n,p to be characterized and a strip at the edge of this sensitive surface. The discrete points define a matrix grid in this area. The characteristic function of the photosensitive cell is defined on a surface or area having dimensions substantially greater than those of the sensitive area of the photosensitive cell. The definition of this substantially greater area is the result of charge leaking between adjacent photosensitive cells and other physical phenomena.
Respective electrical signals R.sub.xi,yj are obtained at the output of the analyzer 13 for these several positions (xi,yj) and the amplitudes of the electrical signals are stored in the calculator in the form of a matrix ##EQU6##
Calculation of differential slopes in x and then in y is performed for each of the elements of the matrix function ##EQU7## thereby obtaining a matrix of values approximating the characteristic function C(x,y) at respective points (xi,yj). Smoothing this matrix of values yields the required characteristic function C (x, y).
The aforementioned calculation and smoothing steps can be interchanged. In this case a function defined by the previously mentioned continuous function R.sub.u,v is obtained by smoothing the matrix ##EQU8##
The characteristic function C(x,y) is deduced from this continuous function R.sub.u,v by double partial. differentiation of R.sub.u,v with respect to x and y.
Accordingly, the prior art is restricted to characterizing a discrete optical member in the form of one or more photosensitive cells, for example. The function of a photosensitive cell is to convert incident light energy into electrical energy. One known form of photosensitive cell is the photodiode. This is in the form of a junction between a p-doped silicon substrate and a thin diffused area of n-doped silicon, the junction being covered with an insulative layer of silicon oxide.